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A regression model for the conditional probability of a competing event: application to monoclonal gammopathy of unknown significance


Arthur Allignol, Freiburg Center for Data Analysis and Modelling, University of Freiburg, Eckerstrasse 1, Freiburg 79104, Germany.


Summary.  Competing risks are classically summarized by the cause-specific hazards and the cumulative incidence function. To obtain a full understanding of the competing risks, these identifiable quantities should be viewed simultaneously for all events. Another available quantity is the conditional probability of a competing risk, which is defined as the cumulative probability of having failed from a particular cause given that no other (competing) events have occurred. When one event is of a particular interest, this quantity provides useful insights, as it displays a probability adjusted on the other competing events. In certain applications, this interpretation may be preferable to that for the cumulative incidence function in quantifying cause-specific cumulative failure probabilities. The use of the conditional probability has been limited by the lack of a regression modelling strategy. We apply recently developed regression methodology to the conditional probability function and illustrate, by using a data set on patients suffering from monoclonal gammopathy of unknown significance, the insights that are gained from this methodology.